AP EAMCET · Maths · Quadratic Equation
If \(\alpha, \beta, \gamma\) are the roots of \(x^3-2 x^2+3 x-4=0\), then the value of \(\alpha^2 \beta^2+\beta^2 \gamma^2+\gamma^2 \alpha^2\) is
- A \(-7\)
- B \(-5\)
- C \(-3\)
- D \(0\)
Answer & Solution
Correct Answer
(A) \(-7\)
Step-by-step Solution
Detailed explanation
If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-2 x^2+3 x-4=0\), then \(\begin{aligned} & \alpha+\beta+\gamma=\frac{2}{1}=2 \\ & \alpha \beta+\beta \gamma+\gamma \alpha=3 \\ & \text { and } \\ & \alpha \beta \gamma=4 \\ & \end{aligned}\) We know that…
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